Yes! About 4 years ago me and my mates decided to go on it one night for a laugh, had some very amusing convos, and I ended up going on it myself a few months later out of general boredom.
Got talking to a guy about Studio Ghibli films, then the conversation went on to other films and tv shows we loved such as HBO shows. We were chatting on Omegle for a couple of hours but I had to go to bed, and he asked for my email address. We talked on msn for months, exchanged numbers and used to chat on the phone, and he sent me some anime dvds in the post, and I sent him some drawings. We always wanted to meet up but lived at opposite sides of the country and the train fares were far too much. We started to drift apart after a year or so of talking to each other, but would have a chat once in a while, and we have each other on facebook nowadays and occasionally chat.
There were a lot of weirdos on there who were just like 'asl?' and wanted to talk dirty, and I'd immediately end the convos with them. I gather that sex chat is all Omegle is used for nowadays so don't think I'll be going on it again....